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Strichartz estimates for wave equations with coefficients of Sobolev regularity. (English) Zbl 1098.35036

There is a contribution in the frame of general investigations regarding Strichartz type estimates for wave equations with nonsmooth coefficients. The strategy is to obtain estimates on components of the solution whose Fourier transform is highly localized. The coefficients of the wave operator should lie in a Sobolev space of sufficiently high order. Using the “wave packets technology” i.e. frame of \(L^2\) functions suited for analysis of wave operators one constructs a parametrix for the wave operator that is suitable for proving estimates. In the last two sections of the paper estimates via parametrix and via truncation/rescaling are shown.

MSC:

35B45 A priori estimates in context of PDEs
35L05 Wave equation
35B65 Smoothness and regularity of solutions to PDEs
35R05 PDEs with low regular coefficients and/or low regular data
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